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`int_(0)^(a) x (1-x)^(5)dx=........`A. `(1)/(5)`B. `(1)/(42)`C. `(1)/(13)`D. `(13)/(42)` |
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Answer» Correct Answer - B Let `I = int_(0)^(1) x (1 - x)^(5) dx` put `1 - x = t implies x = 1 - t` `implies - dx = dt` `implies dx = - dt` When x = 0, then t = 1 and When x = 1, then t = 0 `:. I = int_(1)^(0) (1 - t) (t)^(5) (-dt) = int_(0)^(1) (t^(5) - t^(6)) dt` `= ((t^(6))/(6) - (t^(7))/(7))_(0)^(1) = (1)/(6) (1)^(6) - (1)/(7) (1)^(7)` `= (7 - 6)/(42) = (1)/(42)` |
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